钻井轨道设计问题的有解判别图研究

在求解钻井轨道设计问题的各种数值迭代算法中,不仅计算量大、计算速度慢,而且难以准确判断设计问题是否有解,有几个解。为了解决这个问题,提出了使用拟解析解方法来绘制有解判别图的图示法,通过计算设计方程组的特征多项式的全部实数根,绘制出设计方程组某些正约束未知数的连续变化曲线。通过对比这些连续变化曲线与特征多项式全部实数根的相对位置关系,可以直观地对轨道设计问题解的情况的程序判断结果进行交叉验证。通过对实际设计算例的有解判别图的分析,证实了有解判别图对于设计问题解的存在性判断的正确性。在轨道设计的计算机软件中,有解判别图可以以图形方式直观地向用户展示特征多项实数根与设计问题真解之间的内在关系,有助于用户对设计问题解的存在性做出正确判断。     

限定稳斜角的三维定向井轨道设计问题的求解

为快速、可靠地求解限定稳斜角的三维井眼轨道设计问题,研究了该问题设计方程组的解析求解方法。经过数学公式推导,求出了设计方程组的拟解析解。从理论上证明了从设计方程组出发,可以推导出一个只含有一个未知数的特征函数;而设计方程组的所有未知数,可以由该特征函数的全部实数根和一组解析计算公式依序逐个计算出来。理论分析和实际计算表明,新方法可快速判断设计方程组是否有解,并能在有唯一解和多个解的情况下,快速、准确地计算出该唯一解或全部解。新方法完全克服了初值依赖性、收敛性、不能求多个解等数值迭代类算法的固有缺陷;计算精度只与特征函数求实数根算法有关,是一种几乎精确的算法。研究结果表明,新方法是求解设计方程组快速、可靠、精确的先进计算技术,不仅是算法研究上的理论创新,而且在钻井软件开发上具有很高的实用价值。     

三维悬链线轨道设计的改进算法

三维悬链线轨道设计是新近提出的一种大位移井轨道设计新方法,由于需要使用数值积分法来计算井段增量,设计约束方程组的数值求解比较困难.求出了垂深增量积分式的原函数,得到了垂深增量的解析计算公式.使用该解析公式,求出了约束设计方程组的一个近似解,可以将它作为求解该方程组的迭代法的初始值；使用该解析公式,还证明了稳斜井段的段长与悬链线特征参数之间存在线性相关性,并将这种线性相关性用于设计约束方程组的降维处理,使得原来的具有3个独立未知数的设计约束方程组简化为具有2个独立未知数,从而降低了该方程组的求解难度.垂深增量公式还被用于简化方程组求解过程中的隐含未知数的递序计算,大量减少了数值积分的计算量.使用数论网格迭代法求解降维后的设计约束方程组,不仅计算过程稳定、可靠,而且易于计算机编程实现.     

三维悬链线轨道设计的数值算法

有学者提出了考虑方位漂移的三维悬链线轨道设计问题,并建立了数学模型和数值求解的基本思路,为方位漂移轨道设计技术的应用提供了理论框架,但对求解数学模型的实际算法描述不甚清晰,有可能影响其在大位移井工程设计实践中的广泛应用。考虑方位漂移因素的设计约束方程组是一个具有3个独立未知数、多个隐含未知数的非线性方程组,需要使用数值迭代法才能求出其数值解。给出解析形式的垂深增量公式,利用约束方程组中的垂深方程,将3个独立未知数中的一个表示为其他未知数的函数,从而使设计约束方程组可以降维为二元非线性方程组,降低了数值求解的规模和难度。结合隐含未知数的递推计算策略,采用缩半网格法能可靠地求出降维后的设计约束方程组的数值解,特别适用于计算机编程实现。     

大位移井侧位抛物线剖面设计的数值计算

侧位抛物线剖面是大位移井轨道设计中常用的剖面类型。对侧位抛物线剖面设计求解过程中的求侧位抛物线初始点井斜角的数值方法和从段长求井斜角的数值方法进行了分析,指出其关键是求解侧位抛物线初始点井斜角所满足的一个三角函数方程。用倍角公式可将该三角函数方程转化成一个四次代数方程,然后用求根公式直接求出解析解。用解析解可简化侧位抛物线剖面设计过程,减少计算工作量,提高计算速度。侧位抛物线井段参数计算中需要通过段长公式来反求井斜角,给出了反求井斜角的二分法。本文的算法可应用于大位移井轨道设计的软件开发。     

二维阶梯形水平井段设计方法研究

阶梯形水平井段用于开发层叠状的多个油层,比用多口水平井来开发具有节省钻井投资、提高开采效率等优点.建立了阶梯形水平井段所满足的二元非线性方程组,对于常用的5种不同的未知数组合情况,使用数学化简技巧将该方程组归结为3种标准形式的三角函数方程组.推导出了3种标准形式方程组的解析解计算公式.在求解阶梯形水平井段设计问题时,增降斜井段的拐点处的井斜角是一个关键未知数,而油层井段的长度、增(降)井段的井眼曲率可以作为另一个未知数.以某水平井开发2个不同深度的薄油层为算例,对计算公式进行了验证,并与文献上的数据进行了对比,证实了计算公式的正确性.计算公式具有与具体未知数组合情况相对独立的特点,更有利于计算机软件开发时的模块化编程实现.     

井眼方向控制设计的新方法

为了简化井眼方向控制设计的数学公式推导和施工参数求解,采用矢量代数方法对空间圆弧模型进行了再研究,推导出装置角、井眼方向矢量、井眼高边矢量、圆弧内法向矢量之间的矢量关系式。将圆弧井段参数计算中原来用三角函数表示的复杂公式用简单的矢量公式重新进行描述,极大地简化了有关的公式推导过程和计算。使用新的矢量公式对井眼方向控制方案设计参数求解问题进行研究,求出了全部9种已知设计条件下的设计方案的解,并给出判断初始装置角正负符号的新的、简单的判据。使用实际数据对设计方法进行测试,结果完全正确。给出的圆弧模型参数矢量计算公式,具有较强的几何直观性,比其他使用三角函数的相关公式更加简单,不仅可以用于解决井眼方向控制问题的求解,而且在圆弧型井眼轨道设计与计算的其他问题中都有应用价值。     

水电站库群系统优化补偿调节模型及算法

本文提出的最优补偿调节方法,先将求解复杂的补偿调节优化模型转化为判别约束方程组是否有解的判别问题,进而将该判别问题转变为求解具有简单目标函数的虚拟优化问题,再利用大系统目标协调算法求出最优化补偿调节方案。     

待钻轨道设计问题谱集的数值算法

已知设计参数谱集表征了待钻轨道设计问题中已知设计参数与设计问题的解数之间的复杂数学关系,对于指导钻井设计人员快速完成设计工作具有较大的帮助,可以减少反复调整设计参数的次数,提高设计效率,但是通常难以用数学表达式进行描述。为了解决这个难题,提出了已知设计参数谱集的新概念,建立了谱集理论的研究框架。通过数理公式推导给出了谱集的数值计算方法,该算法能够求出谱集的边界曲线。算法参数影响因素分析表明,合理设置解的约束条件可以产生更合理的谱集,其中方位角约束条件对谱集的影响最大。实际算例应用表明,参照谱集进行井眼轨道设计可以避免钻井设计人员反复调整设计参数、计算无解的现象,极大地提高设计工作效率;同时,该算法也可用于钻井轨道设计软件的开发,具有较重要的实用价值。     

侧斜井剖面优化设计方法

A油田套损井累计占生产井数的15.1%,为了不影响原来的井网部署和开发方案,减少钻井占地面积及成本,可采用侧斜工艺技术进行套损井的修复。综合考虑A油田老井网的特点,结合侧斜井现场施工的实践,确定了侧斜井剖面设计的井身质量的一般原则:全井井眼曲率小于1.5°/30m,最大井斜角不超过3°,设计水平位移不能大于30m;侧斜井的井身剖面选用"直井段-侧斜段-稳斜段-降斜段",将最大井斜角定为已知,设计方位与原井眼方位相反。指定井身剖面设计方程组的4个参数为已知设计参数,求出方程的解析解,并利用该解析解研究了最大井斜角和井眼长度随造斜点的变化规律,提出了以造斜点为优选变量的优化设计算法。实际算例表明,该优化设计方法可以使用很少的计算量,快速求出满足井身质量要求的最优设计参数和最优设计剖面。     

纠偏轨道设计的初始装置角允许值计算

在实钻过程中,纠偏轨道的设计参数必须满足一定的约束条件,才能设计出满足施工要求的纠偏轨道。以中靶约束为条件,建立了纠偏轨道设计参数的几何模型,推导出了单圆弧纠偏轨道设计参数的计算公式,给出了初始装置角允许取值范围上、下界限值的计算方法。通过算例验证了该算法的合理性和正确性,可将所有满足设计约束条件的初始装置角和井眼曲率绘制成设计参数允许取值范围图。当初始装置角和井眼曲率取值于该图的设计参数允许取值范围内,能够保证待钻设计轨迹满足井身参数的要求。本文的数学推理过程可进一步推广到定向井的圆形或椭圆形靶的情况,只需将圆弧平面与靶窗平面的交线扫过的范围修改成该交线与圆形或椭圆形靶的切点之间的范围。软件开发及其在实钻井眼轨迹监控中的应用表明,设计参数允许取值范围图可减少纠偏轨道设计的盲目性,提高设计质量。     

Multiple Distributed Generators for Distribution Feeder Voltage Support

Inclusion of voltage support distributed generation (VSDG) can reinforce the feeder voltage of distribution networks, especially in rural/remote areas where voltage dip and frequent blackouts are significant concerns for power utilities. However, installation of multiple distributed generators within a distribution grid system may introduce technical problems in network operation and control, including control interaction and/or voltage instability. This paper addresses the network issues that may occur during multiple VSDG inclusion in the network and presents analytical models and solutions to develop design criteria of VSDG installation in the networks. Voltage sensitivity of lines is investigated and the effect of DG real (P) and reactive (Q) power injections with Q priority is developed for optimal use of VSDG in correcting the network voltage. Interaction among VSDG controllers has been explored and a generalized model is presented to analyze this interaction between any number of VSDGs in the network. The model is tested on a sample VSDG system and test results are presented. The issue of which VSDG must be started recognizing the costs of starting is addressed using an inverse definite minimum time (IDMT) model. A prioritization and coordination scheme for start discrimination of multiple VSDGs is proposed which avoids hunting between multiple generators.     

Direct borohydride fuel cell: Main issues met by the membrane–electrodes-assembly and potential solutions

The direct borohydride fuel cell (DBFC) is a fuel cell for which there is consensus about its promising commercial future as a portable power system. However, its development faces three main issues: the borohydride hydrolysis (issue 1) and crossover (issue 2), and the cost (issue 3). These issues are encountered by the membrane–electrodes-assembly. By a discussion around these three issues, the present paper reviews the experimental aspects. The discussion stresses on the opportunities of improvements and reviews the potential solutions that are proposed in the open literature. For each issue, the best solution seems to be a combination of improvements. The issue 1 may be solved thanks to a gold-based anode catalyst and an optimized fuel. The solution to the issue 2 may be a more efficient membrane combined with an optimized fuel and an inactive-towards-borohydride cathode catalyst like MnO₂. Regarding the issue 3, cheaper materials and better fuel use efficiency are the keys. The DBFC is still in a development phase with a small number of years of R&D invested and it appears that there are real improvement opportunities on the path of the DBFC marketing.     

Mass and heat transfer study in solids of revolution via numerical simulations using finite volume method and generalized coordinates for the Cauchy boundary condition

This paper proposes a numerical solution for the diffusion equation with convective boundary condition applied to solids obtained through the revolution of arbitrary bi-dimensional geometries, using generalized coordinates. The diffusion equation was discretized using the finite volume method, with a fully implicit formulation. The solution exploits symmetry conditions and that decreases the computational effort demanded, in comparison to the traditional use of three-dimensional grids. The proposed solution was used to describe diffusion processes which have a well-known solution. There was a good agreement among the results obtained through the proposed solution and the correspondent analytical solutions, as well as the experimental data.     

Analytical study of steady-state compressible flow of perfect gas with constant heat flux and friction in constant area ducts

Exact analytical solutions of one-dimensional gas dynamics are intensively applied in engineering practice as a tool in modelling and simulating the piping systems that utilize a compressible medium as their working fluids. Well-known exact analytical solutions for simple types of flows, i.e. for flow processes in which only a single effect is taken into account (e.g. such limiting cases of flows as isentropic, adiabatic or isothermal), are classics of modern one-dimensional gas dynamics theory formed in the first half of last century. At present, gas dynamics does not possess an exact analytical solution for more than a single factor bringing about changes in fluid properties. In this paper the possibility of obtaining general and particular solutions of a non-linear ordinary differential equation (ODE) system describing one-dimensional steady-state flow of compressible ideal gas in constant area ducts with a constant heat flux and friction factor is discussed. It shows that ODE system variables can be separated, and integrals can be taken in terms of elementary functions. Since an analytical solution is the most important result of the paper, its detailed derivation is presented. The mathematical properties of the solution are analyzed in order to calculate this type of compressible flow. For the purpose of this analysis, the functions of the solution and duct performance characteristics of the flow model are demonstrated for various flows and heat flux values, as well as distributions of flow parameters along the duct for both subsonic and supersonic flows. The thermodynamic constraints of the solution are also studied. The analytical solution formulas obtained in this paper may serve as a definition of heat flux and friction factor in ducts from a viewpoint of one-dimensional gas dynamics.     

Non-uniform control volume sizing methodology for relative humidity control of proton exchange membrane fuel cells

Real-time water management is a major ongoing challenge for PEM fuel cell technologies. Given the inherently distributed nature of the system, local conditions can change significantly from cell-to-cell. To compensate for this variance, a control-oriented PEM fuel cell model that is capable of capturing localized differences in operating conditions in real time is needed. To fulfill this need, the authors previously investigated the use of multiple, equally sized control volumes (CVs) to represent the cathode channel. This modification to the modeling architecture greatly improved the accuracy over a one CV model, which was incapable of capturing the stack vapor dynamics. However, because the relative humidity distribution in the stack is non-linear, equally sized CVs do not optimize the additional information gained from the multiple cathode CV approach.In this paper, an algorithm to optimally size CVs based on an analytical solution of the relative humidity profile in the cathode channel is presented. The analytical solution was found based on the vapor mass conservation equation in the cathode. This conservation equation includes consideration of electro-osmotic drag, concentration gradient based diffusion, vapor generation, and bulk fluid flow. The solution was validated by correcting the one CV model to match experimental data using the result of the analysis. After applying the analytical adjustment strategy to the one CV model, the dewpoint temperature predicted by the augmented one CV model was in good agreement with experimental results.The solution also revealed a coefficient that relates the current, flow rate, and membrane diffusion in a single term. This coefficient could be used for control decisions to avoid flooding issues in the stack. Furthermore, using the analytical RH profile equation, CVs can be optimally, unevenly sized to improve the modeling of local operating conditions.     

分支井设计中开窗点的计算方法

在煤层气开发中,一般采用多分支、鱼骨型的井眼轨道.在分支井设计中,在完成主井眼轨道设计之后,需要根据地质上给定的开窗点数据在设计轨道上确定相应的设计开窗点井深及井身数据.教科书和有关文献上没有计算开窗点的现成公式,为了开发分支井轨道设计软件的需要,建立了从地质开窗点数据计算设计开窗点井深的优化矢量数学模型;根据稳斜井段和圆弧井段的矢量数学模型,推导出了设计开窗点的井深计算公式,给出了从设计轨道数据计算设计开窗点的算法.经过对某国内油田数十口分支井实际设计数据的检验,本文给出的设计开窗点计算公式和算法具有计算速度快、计算结果准确、容易编程实现等优点.本文的计算公式和算法可用于分支井轨道设计计算机软件的开发编程.     

Formal Fundamental Solutions of Irregular Singular Differential Equations Depending Upon Parameters

Given a system of linear differential equations with a pole, say at z = 0, it is well known that the system has a formal fundamental solution which is the product of a formal power series in a root of z, a matrix power of z, and the exponential of a polynomial in a root of z ^–1. Suppose that the system depends analytically upon several parameters in a neighborhood of some point in the parameter space. Then the question arises whether there exists an analytic formal fundamental solution, i.e., a formal fundamental solution whose coefficients are analytic in the parameters in a possible smaller neighborhood of the given point. In 1985, Babbitt and Varadarajan treated this problem together with that of the deformation of nilpotent matrices over rings. They assume that the exponential parts of the formal fundamental solutions are well behaved in some precise sense. In the present paper I will provide constructive proofs of their theorems on formal fundamental solutions and in this way also improve them slightly. Furthermore I will give a condition for well behaved exponential parts – and hence for the existence of an analytic formal fundamental solution – which can be expressed solely in terms of the given equation.